Questions tagged [quantum-chemistry]
The quantum-chemistry tag has no usage guidance.
243
questions
0
votes
0answers
12 views
Adiabatic vs diabatic molecular surfaces
I am a bit confused about the quantum numbers in the case of diabatic potential energy curves (PEC) for diatomic molecules. Below it is a figure from this paper that I will be referring to. So as far ...
1
vote
1answer
51 views
Lagrangian of a Hydrogen Atom
So in classical mechanics, we can generally convert from the Hamiltonian to the Lagrangian and back using Legendre transformations. However, I have found this to be a bit troublesome in QM. ...
0
votes
0answers
19 views
Expectation Value of an Operator in the Projector Augmented Wave Method
I'm starting on DFT and came across this technique called PAW Wave Method for multi atoms system wave function. It is a widely employed method in DFT calculations.
From the attached picture, I'm ...
5
votes
1answer
107 views
Creation and Annihilation Operators In the Hydrogen Atom
In my quantum chemistry course, we have been discussing the wavefunctions of the hydrogen atom, further, I am familiar with the idea of ladder operators from the QHO. Can we use ladder operators to ...
0
votes
0answers
21 views
Theoretical origins of optical rotation
I'm not sure if I searched this with as fine-toothed a comb as I should have, but I found nothing online. I wanted to know if someone could point me to outlets wherefrom I could learn about the ...
0
votes
2answers
55 views
Attraction and repulsion between atoms
In six east pieces Richard Feynman describes atoms as little particles that move around in perpetual motion attracting each other when they are a little distance apart but repelling upon being ...
0
votes
0answers
14 views
Momentum space Hartree-Fock overlap matrix
I was looking at Hartree-Fock studies of systems like twisted bilayer graphene, see for example: https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.031034. Here, the orbitals chosen are eigenstates ...
0
votes
0answers
34 views
Why exactly do bonds form?
From my solid state physics class I know about all the various types of bonds and the mechanisms that cause them. Let's leave the specific physics aside for now and just accept that a bond lowers the ...
3
votes
2answers
177 views
Energy level splitting in two-state systems
I was learning basic quantum mechanics using Feynman Lectures on Physics. In Chapter 8 Feynman has described ammonia inversion due to tunnelling. Feynman has first used the base states as the two ...
3
votes
0answers
28 views
Does the region inside of buckyball have a slightly negative energy density due to the casimir effect?
I was considering a buckyball floating in a vacuum.
It's surface is a strongly conducting surface and so I would expect some kind of Casimir effect to apply, i.e. the wavelength of virtual photons ...
1
vote
1answer
27 views
Do the 'fine transitions' of electrons in a molecule or atom involve jumps between sublevels within a 'level', e.g. from $s$ to $d$?
Hyperfine transitions, like the (astronomically) famous 21cm line, involve just spin flips, right?
And the electron jumps we first learn about in school, that release visible or near-visible photons, ...
0
votes
2answers
24 views
Does the intrinsic spin of electrons change when we excite electrons for hybridisation?
Have had been told that electrons can move from one energy level to another by transmitting or taking in energy, and do that profitably in hybridisation. I am interested in knowing how exactly do they ...
1
vote
0answers
21 views
Cross section for Hydrogen molecule formation
I have been searching for theoretical articles that calculate the hydrogen formation cross section $\sigma(H+H \rightarrow H_2)$, but I found nothing. Can anyone suggest me articles or computer ...
0
votes
0answers
8 views
Dissociation probability vs ionization probability
Suppose we have a diatomic molecule whose ionization energy is $I$ and dissociation energy is $D$ such that $I>D$.
Now suppose an electron with energy $E>I>D$ collides with this molecule. ...
0
votes
0answers
20 views
Why do molecules showing a pure rotational spectra require a permanent dipole?
I understand that pure rotational spectra only exist for molecules which have a permanent dipole moment. The common explanation is "so that they can interact with the E-field of the incoming ...
1
vote
2answers
45 views
Why do molecules absorb “exact” frequencies when given a “continuous” beam of light?
This question is in the context of performing simple rotational spectroscopy on molecules, but could be extended for more general cases.
In rotational (microwave or IR) spectroscopy of molecules, the ...
0
votes
1answer
47 views
Electric quadrupole allowed transitions mathematical proof
Consider the electric quadruple moment operators as follows:
$Q_{20} = \frac{e}{2}(x^2+y^2-2z^2) $
$Q_{2 \pm1} = \frac{e\sqrt{6}}{2}z(x\pm iy) $
$Q_{2 \pm2} = - \frac{e\sqrt{6}}{4}(x\pm iy)^2 $
I ...
2
votes
0answers
38 views
Is a solution to the Hartree-Fock equations guaranteed to exist? Is it a Slater determinant in any basis?
My understanding is that the Hartree-Fock equations can be derived from the variational theorem as follows:
The variational theorem states that for an arbitrary wavefunction $|\psi \rangle$, $\langle \...
1
vote
2answers
40 views
Why two orbitals having same phase is not a random phenomenon?
I have been reading about Molecular Orbital Theory for Chemistry.
I tend to believe that when two Hydrogen atoms approach each other, whether the $1s$ orbitals are in-phase or out-phase is a random ...
0
votes
0answers
58 views
General form of Hartree-Fock potential
$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}$
I ...
14
votes
1answer
360 views
Why does Hartree-Fock work so well?
Why does the Hartree-Fock method for electronic structure work so well for atoms?
More specifically, why is the "correlation energy" a relatively small component of an atom's (ground state) ...
0
votes
0answers
20 views
Calculating surface charge in Thomas-Fermi layer
My understanding is that chemical potential at the surface of a bulk crystal is concentrated at, and would be described by, the Thomas-Fermi Layer (see Ad-atoms and underpotential): https://www....
3
votes
0answers
31 views
Irreducible representation of derivatives of diabatic electronic wave functions
My question regards the symmetry properties of the derivatives of diabatic electronic wavefunctions. I think the question goes somewhat beyond the standard group theoretical machinery taught in ...
2
votes
3answers
114 views
How to distinguish the $p_x$, $p_y$, $p_z$ orbitals when one can choose the $x-$, $y-$, and $z-$ axes arbitrary?
How to distinguish the $p_x$, $p_y$, $p_z$ orbitals since one could choose the $x-$, $y-$ and $z-$axes arbitrary?
How could the can the wavefunctions that describe the probability of the presence of ...
0
votes
0answers
29 views
Widespread false formulation of Hunds 1. rule
According to Wikpedia Hunds first rule says
Hunds 1. rule, Wikipedia: For a given electron configuration, the term with maximum multiplicity ($2S+1$) has the lowest energy.
I would formulate this ...
0
votes
0answers
43 views
Why would one think that a solution of the time-independent Schrödinger equation is in the span of configuration state functions?
I am trying to understand why the hypothesis of configuration interaction methods is valid, i.e. I want to understand why one would think that an $N$-body wave function would be in the span of ...
1
vote
0answers
18 views
Atomic density derivative with respect to nuclear coordinates transformed to all space
Please show that the derivative of some atomic density $\rho_{I}$ with respect to its nuclear coordinate $R_{I}$ can be expressed in terms of its electronic coordinate $|\textbf{r - R}_I|$
$ \frac{\...
2
votes
1answer
36 views
Hydrogen bonding under quantum mechanics
I know that Fermi-Dirac statistics can be used to account for covalent bonding, but how does quantum mechanics explain hydrogen bonding?
0
votes
2answers
63 views
How to interpret Hamiltonian in terms of its matrix representation
I am reading a research paper (A Theoretical Analysis of Zero Field Splitting Parameters of Mn2+ Doped Diglycine Calcium Chloride Tetrahydrate) where they state the Hamiltonian term:
$$H=\frac{F}{180}\...
0
votes
0answers
19 views
Is the $g$-tensor describing the Zeeman effect for molecules always diagonalizable?
The Zeeman splitting of a molecule can be described through the $g$-tensor, which couples the magnetic field to the angular momentum of the molecule. Is the $g$-tensor always diagonalizable?
2
votes
1answer
24 views
Degree of kinetic energy component in Hamiltonian for any molecule
In reading "Density functional theory of atoms and molecules" by Parr and Yang, I was not sure what is meant by this sentence when the Virial theorem was introduced.
Suppose I have a ...
3
votes
1answer
135 views
Casimir effect evidence
How does the attraction between two metal plates support a new effect (or force)?
Isn't it expected that two plates attract each other due to the London dispersion?
If so, how does the experiment ...
2
votes
1answer
45 views
Hybrid Orbitals
https://glossary.periodni.com/glossary.php?page=41&en=high+fructose pictures like the ones in this article make no sense to me.
I understand that we can take solutions to the Schrƶdinger equation ...
0
votes
2answers
61 views
Why do elements want to mimic Nobel gasses so much? [duplicate]
Why is the octet rule true?
How can electrons even stay around nuclei with lesser number of protons?
5
votes
1answer
88 views
How does the Pauli Exclusion principle explain the incompressibility of metals?
The Pauli Exclusion principles states that no two identical fermions can have the same quantum state. In my lecture notes, it is mentioned that this principle helps us explain the fact that metals are ...
1
vote
1answer
37 views
Expression and explanation of quantum mechanical harmonic oscillator
I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Quantum Mechanical Harmonic Oscillator, the author says the following:
Fig. 2....
0
votes
1answer
67 views
Hamiltonian matrix elements involving ladder operators for spin-1 state
I am reading the Doctorate thesis 'Zero-Field Anisotropic Spin Hamiltonians in First-Row
Transition Metal Complexes: Theory, Models and
Applications' (link: https://tel.archives-ouvertes.fr/tel-...
1
vote
0answers
26 views
Two descriptions of Valence Bond Theory
I am trying to understand theoretically Valence Bond Theory from the first principles of Quantum Mechanics and suitable approximations. I am a mathematician with shaky bases in Quantum Mechanics.
...
0
votes
1answer
112 views
Is the $1s^22s^22p^6$ atomic configuration lower in energy than the $1s^22s^22p^5$ atomic configuration?
I read that atoms in the first few rows of the periodic table gain or lose electrons to have 8 valence electrons so that they are energetically stable and has minimum energy.
This means that an atom ...
1
vote
1answer
71 views
Interpretation of occupation numbers and creation-annihilation operators in strongly correlated systems
I hope I am not asking anything stupid, but I am having a hard time interpreting some
(seemingly simple) results.
The simplest approximate form of an $N$-electron wave function (w.f.) is a Slater-...
2
votes
1answer
51 views
Unitary Coupled Cluster Operator
In quantum computing, we always want to deal with unitary evolution operators. That's why the traditional definition of the Coupled Cluster ansatz is modified to the so-called Unitary Coupled Cluster, ...
0
votes
1answer
92 views
Benzene ground state
Iām currently studying my first course on Quantum Physics. Regarding the topic of Sommerfeldās quantization rules, Iāve come across a problem where I was asked whether a benzene molecule would require ...
1
vote
0answers
34 views
Calculation of atomic spectrum
I need to calculate spectrum of Hg atom (wavelength and transition intensity), taking into account relativistic corrections. Can someone suggest a software or a package for atomic spectroscopy, that I ...
2
votes
3answers
207 views
What are the $sp^3$ orbital bond directions relative to a Cartesian reference frame?
When I try to search for this, I find images like below, but it is not clear to me what the actual bond directions are, i.e. the first one appears to be (0, 0, 1) but then I am not sure of the others.
2
votes
1answer
50 views
Quantitative contribution of kinetic and potential energies to the binding energy of the $\sigma$ orbital in $\text{H}_2$ or $\text{H}_2^+$
When a hydrogen molecule forms, 4.52 eV of energy is released, while for $\text{H}_2^+$ the binding energy is 2.77 eV. Such a binding energy is the difference of energies that have four terms in them: ...
5
votes
4answers
287 views
Why does orbital overlap cause attraction?
I have been taught that when orbitals overlap as in $\sigma$ and $Ļ$ bonds, the formation of a bond (which is basically an attraction) takes place. Why does this cause attraction, shouldn't they repel?...
2
votes
1answer
157 views
How to calculate the second-order pertubation in an electron gas?
This problem is from the book Quantum theory of many particles systems by Fetter & Walecka (1971), exercise 1.4.
Problem discription:
The Hamiltonian could be divided into $$H_0=\sum_\limits{\...
4
votes
2answers
238 views
Can you explain DFT and TDDFT functioning (math aside)?
I have been recently reading a lot on the quantum mechanical theory regarding Density Functional Theory, DFT and Time-Dependent Density Functional Theory, TDDFT (Oscillatory and Rotatory Strengths in ...
0
votes
0answers
35 views
Is there an anisotropy factor (g factor) for TDDFT Abs and CD calculations?
Experimentally, anisotropy factor is calculated by dividing the CD spectra by the absorbance spectra multiplying by a factor of 32980 (in order to get a nondimensional quantity)
Theoretical ...
0
votes
2answers
95 views
Is it the Coulomb force which acts between electron and protons creating chemical bonds?
When calculating forces on the atomic level, although Quantum mechanics makes the positions of charged particles"smeared out" is it the Coulomb force which is acting between smeared out electrons and ...
